The present specification includes two (2) CD-ROMs containing computer source code which are referred to herein as Appendix A and Appendix B. The CD-ROMs are duplicates of each other and include the computer source files xe2x80x9cclass_chirp_xform.Cxe2x80x9d that is 8 Kilobytes in size, xe2x80x9cfct_sample.Cxe2x80x9d that is 2 Kilobytes in size, xe2x80x9cchirp_xform.hxe2x80x9d that is 2 Kilobytes in size, and xe2x80x9cLALfct.cxe2x80x9d which is 32 kilobytes in size. The contents of the CD-ROMs are hereby incorporated by reference as if set forth in full herein.
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The present invention relates generally to digital signal processing and more particularly to digital signal processing of quasi-periodic signals whose frequency varies in time.
One application of digital signal processing is the detection and analysis of natural events. Typically, instruments may be used to detect energy released during a natural event. For example, a telescope may be used to gather fluctuating light signals from a star and the fluctuations of light levels may be analyzed to detect small changes in the star""s position caused by an orbiting body. The light levels are transformed into electrical signals by a transducer and these electrical signals are digitized. These digitized signals typically contain a large amount of noise created by the transmission, detection, and transformation of the light levels originating with the star. Digital signal processing methods are typically used enhance the signal to noise ratio so that the actual signals may be detected and analyzed.
Another example of a natural event whose detection and analysis may be greatly enhanced by the use of digital signal processing is the combining of massive bodies such as two neutron stars in a binary system as depicted in FIGS. 1 and 2. The two stars, 10 and 12, orbit each other by their mutual gravitational attraction creating a binary system. The stars are have a significant amount of kinetic energy and angular momentum within the binary system. If the stars are close enough, the motion of the orbiting stars creates a gravitational wave 18 radiating outwards from the binary system. The loss of energy by the stars in the form of gravitational waves causes the stars to spiral in toward each other. As the gravitational wave propagates outward, it causes a gravitational strain that is detectable as an apparent change 22 in the distance 20 between two objects. The gravitational wave may be detected using a Michelson type laser interferometer 26 stationed at the Earth 24. The laser interferometer detects the gravitational wave by measuring the distance between test and reference masses using an interference pattern created by a split, reflected, and recombined laser beam.
FIG. 2 is a graphical depiction of the expected gravitational strain created by an inspiral binary star system versus time. The y axis 28 of the graph represents gravitational strain, h, which is the amplitude of the fractional xe2x80x9cstretchingxe2x80x9d that occurs when a gravitational wave passes. That is, if h were 0.01, there would be a 1% change in the measured distance between two objects along one of the axes transverse to the direction of propagation of the gravitational wave. The actual stretching is small, a maximum of 1 part in 10{circumflex over ( )}18 for most expected astrophysical events. The x axis 30 of the graph represents increasing time.
In the initial inspiral stage, the two binary stars, 10 and 12, approach and spiral towards each other at a greater and greater angular velocity. During the inspiral period, the generated gravitational waves are expected to result in changes in gravitational strain 32 with increasing amplitude and frequency, creating a xe2x80x9cchirpxe2x80x9d signal. Chirp signals are characterized as signals whose frequency changes in time. During the ringdown phase, the merged stars 15 are expected to create gravitational waves that cause changes in the gravitational strain characterized by a damped chirp signal where both the frequency and amplitude of the signal may decrease with time. During the merger phase 13, the inspiralling binary system is expected to generate gravitational waves of currently unknown amplitude and frequency.
Gravitational wave data may be analyzed by preparing templates of expected signal forms and comparing these templates to actual signals using Fourier transforms. For each expected signal, a new template must be created. This means that thousands of templates must be created for each expected type of inspiral event. The creation and use of numerous templates may require extensive computational resources. Therefore, a need exists for a digital signal processing method that does not require extensive template creation and storage. The present invention meets such need.
The present invention provides a digital signal processing technique, a Fast Chirp Transform (FCT), for the enhanced detection and production of quasi-periodic signals. In one embodiment, an quasi-periodic signal is detected in a signal sample by providing a phase function describing a phase term of an expected quasi-periodic signal. A set of contiguous intervals is determined wherein the difference in the phase function between the contiguous intervals is less than or equal to xcfx80 and the difference is substantially constant. A vector of phase coefficients is generated using the phase function with each element of the vector corresponding to a contiguous interval from the set of contiguous intervals. A signal sample is acquired and a dot product between the vector and the signal sample is calculated. The Fourier spectrum resulting from a Fast Fourier Transform on the dot product provides superior signal to noise ratios for detection of the expected quasi-periodic signals.
In one embodiment, a FCT is used to enhance the detection capabilities of a laser interferometer used to detect gravitational waves. In another embodiment, an FCT is used to enhance the detection of radar signals coming from a radar signal transmitter. In another embodiment, an FCT is used to detect a quasi-periodic reflected signal for object detection applications such as radar, sonar, and materials testing. In other embodiments, the inverse of the FCT is used to produce quasi-periodic signals.